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Structural ensemble dynamics based closure model for wall-bounded turbulent flow

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Acta Mechanica Sinica 2009年第5期25卷 731-736页

作者： Zhen-Su She Ning Hu You wu state {2. {3. for turbulence and complex systems and Dept Mechanical and aerospace engineering,College of engineering, peking University,100871 beijing, China state key {2. for {3. and complex systems and Dept Mechanical and aerospace engineering College of Engineering Peking University 100871 Beijing China

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

关键词： turbulence Closure equation Channel flow Structural ensemble dynamics

TWO KINDS OF HARMONIC PROBLEMS IN CONTROL systems

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Journal of systems Science & complexity 2009年第4期22卷 587-596页

作者： Zhisheng DUAN Lin HUANG state key Lab for {2. and {3. systems and department of mechanics and aerospace engineering,College of engineering,peking University,beijing 100871,China. state key Lab for {2. and {3. systems and department of mechanics and aerospace engineering College of Engineering Peking University Beijing 100871 China

This paper discusses the harmonic problems in control systems from two aspects:Oneis the harmonic control among different subsystems,and the other is the harmonic control amongmultiple *** intrinsic problems in such systems are *** is pointed out that somesubsystems must be unstable to stabilize the whole interconnected system by an *** discrete-time multi-input systems,a necessary and sufficient condition is presented for the strictdecrease of the quadratic optimal performance index with the control input *** showsan essential difference between single-input and multi-input control ***,some futureresearch directions are discussed in harmonic control of interconnected systems,allocation of multi-control inputs,fault-tolerant control,and fault-diagnosis.

关键词： Interconnected system quadratic optimal control redundant inputs Riccati equation simplectic matrix.

The refined theory of deep rectangular beams for symmetrical deformation

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Science China(Physics,mechanics & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2.1 College of Science, China Agricultural University, beijing 100083. China 2.{3. {2. laboratory for turbulence and complex systems and department of mechanics and aerospace engineering, peking University, beijing 100871, China College of Science China Agricultural University Beijing 100083 China state key {2. for {3. and complex systems and department of mechanics and aerospace engineering Peking University Beijing 100871 China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method

A computational investigation on random packings of sphere-spherocylinder mixtures

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Science China(Physics,mechanics & Astronomy) 2010年第12期53卷 2284-2292页

作者： LU Peng, LI ShuiXiang , ZHAO Jian & MENG LingYi state key {2. for {3. and complex systems, department of mechanics & aerospace engineering, College of engineering, peking University, {12. 100871, China 1. state key {2. for {3. and complex systems Department of Mechanics & Aerospace Engineering College of Engineering Peking University Beijing 100871 China

Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.3.. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature.

关键词： packing binary mixture sphere spherocylinder packing density aspect ratio

Energy shaping for coordinating internally actuated vehicles

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Theoretical & Applied mechanics Letters 2011年第2期1卷 76-80页

作者： fan wu~(a) and {2. {3.~(b) The state key laboratory for turbulence and complex systems,peking University,beijing 100871,China The state key {2. for {3. and complex systems Peking University Beijing 100871 China

This paper considers the stable coordination problem of two vehicles equipping with internal moving mass *** coordinating and stabilizing control are derived by energy shaping. The proposed method is physically motiva... 详细信息

关键词： moving mass actuator under actuated energy shaping stabilization

The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms

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Science China(Physics,mechanics & Astronomy) 2009年第6期52卷 909-918页

作者： SHEN fang1 & wu WangYi2.1 {2. key laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, beijing 100190, China 2.{2. key laboratory of turbulence and complex {13. & {12. of mechanics and engineering Science, peking University, beijing 100871, China 1. state key {2. for Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing 100190 China 2. state key {2. of turbulence and complex systems & department of mechanics and engineering Science Peking University Beijing 100871 China

Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.

关键词： basic function unstructured grid aneurysm viscous incompressible flow artificial compressibility flux splitting

An Approach to Formation Maneuvers of Multiple Nonholonomic Agents using Passivity Techniques

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An Approach to Formation Maneuvers of Multiple Nonholonomic ...

A new numerical method on unstructured grids

2.09中国控制与决策会议

作者： wu fan,geng zhiyong the state key laboratory for turbulence and complex systems,{2.,{3. University,beijing 100871

＜正＞This paper studies the problem of formation maneuver of multiple nonholonomic agents.A dynamic feedback linearization method is used to transform each agent’s dynamic model into two chains of 3.d order *** a decentralized discontinuous formation control law with inter-agent damping injection is *** stability of the overall system is proved by using Lyapunov *** proposed algorithm is applied to a nonholonomic multi-vehicles formation maneuver simulation,which shows the effectiveness of our strategy.

关键词： Multiple nonholonomic agents Formation Full-state linearization Passivity

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Science China(Physics,mechanics & Astronomy) 2009年第12期52卷 2016-2026页

作者： wu WangYi & XIE WenJun state {2. {3. for turbulence and complex System,department of mechanics and aerospace engineering,College of En-gineering,peking University,beijing 100871,China

A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed. By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.

关键词： basic function scheme new numerical method unstructured grids

ROBUSTNESS ANALYSIS OF LEADER-FOLLOWER CONSENSUS

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Journal of systems Science & complexity 2009年第2期22卷 186-206页

作者： Jinzhi WANG Ying TAN · Iven MAREELS state key {2. for {3. and complex System and department of mechanics and aerospace Engi-neering College of Engineering Peking University Beijing 100871 China. Departmen~ of Electrical and Electronic engineering University of Melbourne Melbourne VIC. 3010 Aus-tralia.

In this paper,robustness properties of the leader-follower consensus are *** of presentation,the attention is focused on a group of continuous-time first-order dynamicagents with a time-invariant communication topology in the presence of communication *** orderto evaluate the robustness of leader-follower consensus,two robustness measures are proposed:the L_2.ain of the error vector to the state of the network and the worst case L_2.gain at a *** L_2.gain of the error vector to the state of the network is widely used in robust control design andanalysis,the worst case L_2.gain at a node is less conservative with respect to the number of nodes inthe *** is thus suggested that the worst case L_2.gain at a node is used when the robustnessof consensus is *** analysis and simulation results show that these two measuresare sensitive to the communication *** general,the 'optimal' communication topology thatcan achieve most robust performance with respect to either of the proposed robustness measures isdifficult to characterize and/or *** the in-degree of each follower is one,it is shown thatboth measures reach a minimum when the leader can communicate to each node in the network.

关键词： Communication errors leader-follower consensus robustness.